Question

triangle abc is shown in the diagram. the lengths of the sides are in terms of the variable n, where n ≥ 4. complete the inequality. m∠□ < m∠□ < m∠□ the triangle has vertices a, b, c. side ab is 3n - 2, side bc is 2n, side ac is n + 3.

Explanation:

Step1: Assign sides to opposite angles

Side opposite ∠A: 2n
Side opposite ∠B: n+3
Side opposite ∠C: 3n-2

Step2: Compare side lengths (n≥4)

• 2n vs n+3: 2n - (n+3) = n-3 ≥1 (2n > n+3)
• 3n-2 vs 2n: 3n-2 -2n =n-2 ≥2 (3n-2 >2n)

Order of sides: n+3 <2n <3n-2

Step3: Relate sides to angles

Smallest side ↔ smallest angle; largest side ↔ largest angle

Answer:

m∠C < m∠B < m∠A